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Kunal Kumar (to be contacted for any queries regarding this model implementation)

kkumar -at- physics.carleton.ca, Carleton University

In collaboration with

Katy Hartling

khally -at- physics.carleton.ca, Carleton University

Heather E. Logan

logan -at- physics.carleton.ca, Carleton University

Model Description and Implementation

The Georgi-Machacek (GM) model was proposed in 1985 [1] as a plausible scenario for EWSB with interesting collider signatures. In this model, the scalar sector of the Standard Model (SM) is extended by the addition of one complex and one real SU(2) triplet. The hypercharge assignments of the triplets allows for a custodial SU(2) symmetry to be imposed upon the scalar potential, so that rho=1 is preserved at tree level. This is desirable for SM extensions in light of constraints from electroweak precision data. The model has the following salient features that make it phenomenologically interesting:

the hVV (and hhVV) coupling can be enhanced compared to the SM

the presence of additional scalars (including doubly charged ones)

The GM model can thus be a useful benchmark for the study of Higgs properties as well as searches for additional scalars.

The doublet vev and the triplet vevs are constrained by
to ensure the model generates the measured W and Z boson masses. We parametrize the relative size of the vevs by

The scalars (apart form Goldstone bosons) in this model can be classified as two custodial SU(2) singlets, a triplet and a fiveplet. The two custodial singlets mix by an angle alpha to give eigenstates h and H, one of which is the 125 GeV Higgs.

We follow Ref. [2] to implement the most general scalar potential that conserves custodial SU(2). It is automatically CP-conserving. The parameters of the potential are denoted by
mu2sq, mu3sq, lam1, lam2, lam3, lam4, lam5, M1coeff and M2coeff in the .fr file. We trade three of these to obtain the set of 9 external parameters (mh, Gf, tanth, lam2, lam3, lam4, lam5, M1coeff, M2coeff) in the .fr file that define the scalar potential.

The GM Lagrangian implementation is based on the SM implementation (SM. fr v 1.3).
In addition to the scalar potential, we modify all the relevant SM Lagrangian terms
that change in the GM model (e.g.: Scalar Kinetic Terms, Yukawa couplings).

We also provide the CalcHEP and MG5 model folders generated from the .fr file (feynman gauge was chosen for
generating both these model folders).
In the case of MG5, event generation can be simplified by using the program GMCALC (description below) to generate
a param_card.dat file. (Note that the widths of t, W+, h and additional scalars should be updated in MG5 using the compute_widths option.)